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Geometry Mind Map: Parallel Lines.
Neverwinter Niights: Ms Dulcimae.
From the third house she heads round to the northeast perimeter of the Peninsula District where she kills a few escaped prisoners who are harassing a woman she would subsequently know to be Ms Dulcimae. Zanzi cannot believe this unarmed woman was out in the streets with no one to protect her.
Zanzi: "Who are you? What are you doing on the streets?"
Ms Dulcimae explains that she's a maid for Lady Tanglebrook and was on her way to work earlier in the day when all the prisoners started running riot in the streets. She then confirmed what Gate Captain Kipp had said about the head gaoler Alaefin letting the prisoners go free: "He's a good man," she said, "Why, he'd meet every afternoon in the tunnels with Lady Tanglebrook for a friendly game of chess... They're cousins, you know ...".
Zanzi: "Tunnels, what tunnels?"
Ms Dulcimae: "Lady Tanglebrook has always been leery about walking the streets in this district. Alaefin built the tunnels between the prison and her estate so they could continue their games there. Now that the plague is everywhere, they hoped that continuing to use the tunnels would prevent her from being exposed to it."
After Zanzi enquired where the Tanglebrook Estate was located (it's at the northern shore), Ms Dulcimae requested that Zanzi check in on Lady Tanglebrook to make sure she was okay. "Scared or no," said Ms Dulcimae, "I know she keeps a spare key hidden under her doormat for us."
Obviously this woman cannot be left to fend for herself in these circumstances, so Zanzi offers to escort her to the district gates so that she can inform Gate Captain Kipp of what she has seen. On escorting Ms Dulcimae safely to the district gates the game shifts Zanzi's alignment 3 points towards Good. She is now of Neutral alignment 63; when this alignment reaches 70 she will change from Neutral to Good, meaning that she will gain more respect from NPC's but may find the cost of purchasing items more expensive than she would have if storekeeps feared her with an Evil alignment.
In order to judge whether this woman is telling the truth Zanzi uses the Parallel Line theorem, which states that if two lines are parallel then a transverse line will show that the alternate interior angles are congruent, the alternate exterior angles are congruent and the corresponding angles are congruent. She turns on her wire-frame vision to analyse the eyes of Ms Dulcimae, and in each eye Zanzi finds a pair of lines which might be parallel. Selecting Ms Dulcimae's left eye, Zanzi projects a transversal into the eye so that it appears to be coplanar to the lines she is interested in. She then measures the alternate interior angles and finds them congruent, proving that the lines are parallel and that Ms Dulimae's account is genuine. Zanzi could also have measured the alternate exterior angles or the corresponding angles to test whether the lines were parallel, but she had no need to do so because as the alternate interior angles are congruent then the alternate interior angles will be congruent and the corresponding angles will also be congruent. (Zanzi could also have used a branch of mathematics known as topology to come to the same conclusion about Ms Dulcimae, but that is for later study).